Statistics Mean, Median and Mode
for Ungropued Data and for Grouped Data

Ungrouped Data (Raw Data): The information collected
systematically regarding a population or a sample survey is called an ungrouped
data. It is also called raw data.

Grouped Data (Classified Data): When a frequency distribution
is obtained by dividing an ungrouped data in a number of strata according to
the value of variate under study, such an information is called gruoped data or
classified data.

Measures of central tendency:
There are several measures of central tendency. Out of these, the following 3
are used more often
1. Mean, 2. Median and 3. Mode

Median of ungrouped data:
If the observations of an ungrouped data are arranged in increasing or
decreasing order of their magnitude, a value which divides these ordered
observations into two equal parts is called the median of the data. It is
denoted by M.

If the number of observations (n) is an
odd integer, then
M = Value of (n+1)/2 th observation in the arrangement of
observations in increaseing order.

If the number of observations (n) is
an even integer, then
M = (Value of n/2 th observation + Value of (n/2
+ 1) th observation)/2